Musical instruments produce sound through resonance. Woodwind and brass instruments use a volume of air as a resonant cavity. In acoustics, a cavity is a volume of space enclosed by boundaries that contain and reflect sound. When many frequencies are present in a sound, frequencies that are resonant absorb and hold energy far more effectively than other frequencies. Within a few dozen oscillations—fractions of a second!—the energy in noise at all frequencies has been channeled into the amplitudes of only the resonant frequencies, which then dominate the sound.
Resonant modes of pipes
The resonant modes of a cavity correspond to standing waves of air pressure that occur at specific frequencies. For a pipe that is closed at both ends, the resonant modes have nodes at the boundaries. For an open pipe, the resonant modes have antinodes at the ends. In both cases, the resonant frequencies are integer multiples of the fundamental. For a pipe that is closed at one end and open at the other the boundaries are a node and an antinode, respectively. An open/closed pipe has resonances that are only odd-integer multiples of the fundamental. The frequencies and wavelengths of the first four harmonics are shown below.
The size of a vibrating object affects its natural frequency through resonance. For example, the pipes in a pipe organ are made in all different sizes, each designed to produce a specific wavelength and frequency of sound.